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const std = @import("std");
const math = std.math;
const testing = std.testing;
const Vector = @import("vector.zig").Vector;
pub fn Matrix(comptime N: usize) type {
return packed struct {
const Self = @This();
pub const Scalar = f32;
values: [N][N]Scalar,
/// Initialies a matrix.
pub fn init(values: [N][N]Scalar) Self {
return .{ .values = values };
}
/// Creates a matrix filled with the given value.
pub fn filled(n: Scalar) Self {
var result: Self = undefined;
comptime var i = 0;
inline while (i < N) : (i += 1) {
comptime var j = 0;
inline while (j < N) : (j += 1) {
result.values[i][j] = n;
}
}
return result;
}
/// A zero initialized matrix.
pub const ZERO: Self = comptime Self.filled(0);
/// An identity initialized matrix.
pub const IDENTITY: Self = comptime brk: {
var result: Self = undefined;
comptime var i = 0;
while (i < N) : (i += 1) {
comptime var j = 0;
while (j < N) : (j += 1) {
result.values[i][j] = if (i == j) 1 else 0;
}
}
break :brk result;
};
/// Transposes this matrix
pub fn transpose(self: Self) Self {
var result: Self = undefined;
comptime var i = 0;
inline while (i < N) : (i += 1) {
comptime var j = 0;
inline while (j < N) : (j += 1) {
result.values[j][i] = self.values[i][j];
}
}
return result;
}
pub fn invert(src: Self) ?Self {
// https://github.com/stackgl/gl-mat4/blob/master/invert.js
const a = @bitCast([16]f32, src.values);
const a00 = a[0];
const a01 = a[1];
const a02 = a[2];
const a03 = a[3];
const a10 = a[4];
const a11 = a[5];
const a12 = a[6];
const a13 = a[7];
const a20 = a[8];
const a21 = a[9];
const a22 = a[10];
const a23 = a[11];
const a30 = a[12];
const a31 = a[13];
const a32 = a[14];
const a33 = a[15];
const b00 = a00 * a11 - a01 * a10;
const b01 = a00 * a12 - a02 * a10;
const b02 = a00 * a13 - a03 * a10;
const b03 = a01 * a12 - a02 * a11;
const b04 = a01 * a13 - a03 * a11;
const b05 = a02 * a13 - a03 * a12;
const b06 = a20 * a31 - a21 * a30;
const b07 = a20 * a32 - a22 * a30;
const b08 = a20 * a33 - a23 * a30;
const b09 = a21 * a32 - a22 * a31;
const b10 = a21 * a33 - a23 * a31;
const b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (std.math.approxEqAbs(f32, det, 0, 1e-8)) {
return null;
}
det = 1.0 / det;
const out = [16]f32{
(a11 * b11 - a12 * b10 + a13 * b09) * det, // 0
(a02 * b10 - a01 * b11 - a03 * b09) * det, // 1
(a31 * b05 - a32 * b04 + a33 * b03) * det, // 2
(a22 * b04 - a21 * b05 - a23 * b03) * det, // 3
(a12 * b08 - a10 * b11 - a13 * b07) * det, // 4
(a00 * b11 - a02 * b08 + a03 * b07) * det, // 5
(a32 * b02 - a30 * b05 - a33 * b01) * det, // 6
(a20 * b05 - a22 * b02 + a23 * b01) * det, // 7
(a10 * b10 - a11 * b08 + a13 * b06) * det, // 8
(a01 * b08 - a00 * b10 - a03 * b06) * det, // 9
(a30 * b04 - a31 * b02 + a33 * b00) * det, // 10
(a21 * b02 - a20 * b04 - a23 * b00) * det, // 11
(a11 * b07 - a10 * b09 - a12 * b06) * det, // 12
(a00 * b09 - a01 * b07 + a02 * b06) * det, // 13
(a31 * b01 - a30 * b03 - a32 * b00) * det, // 14
(a20 * b03 - a21 * b01 + a22 * b00) * det, // 15
};
return Self{
.values = @bitCast([4][4]f32, out),
};
}
/// Multiplies 2 matrices together.
pub fn mul(self: Self, other: Self) Self {
var result: Self = undefined;
const a = self.transpose();
const b = other;
comptime var i = 0;
inline while (i < N) : (i += 1) {
comptime var j = 0;
inline while (j < N) : (j += 1) {
const row: @Vector(N, Scalar) = a.values[j];
const column: @Vector(N, Scalar) = b.values[i];
const products: [N]Scalar = row * column;
var sum = @floatCast(f32, 0);
comptime var k = 0;
inline while (k < N) : (k += 1) {
sum += products[k];
}
result.values[i][j] = sum;
}
}
return result;
}
/// Multiplies 2 matrices together.
pub fn mulAssign(self: *Self, other: Self) void {
const a = self.transpose();
const b = other;
comptime var i = 0;
inline while (i < N) : (i += 1) {
comptime var j = 0;
inline while (j < N) : (j += 1) {
const row: @Vector(N, Scalar) = a.values[j];
const column: @Vector(N, Scalar) = b.values[i];
const products: [N]Scalar = row * column;
var sum = @floatCast(f32, 0);
comptime var k = 0;
inline while (k < N) : (k += 1) {
sum += products[k];
}
self.values[i][j] = sum;
}
}
}
const VecN = Vector(N);
pub fn apply(self: Self, vec: VecN) VecN {
var result: VecN = undefined;
comptime var i = 0;
inline while (i < N) : (i += 1) {
result.values[i] = 0;
comptime var j = 0;
inline while (j < N) : (j += 1) {
result.values[i] += self.values[i][j] * vec.values[j];
}
}
return result;
}
};
}
fn expectMatrixEqual(comptime N: usize, expected: [N][N]f32, actual: Matrix(N)) void {
comptime var i = 0;
inline while (i < N) : (i += 1) {
comptime var j = 0;
inline while (j < N) : (j += 1) {
testing.expectEqual(expected[i][j], actual.values[i][j]);
}
}
}
test "matrix initialization" {
const A = Matrix(2).init(.{ .{ 1, 2 }, .{ 3, 4 } });
expectMatrixEqual(2, [2][2]f32{ .{ 1, 2, }, .{ 3, 4 } }, A);
}
test "matrix zero" {
expectMatrixEqual(3, Matrix(3).filled(0).values, Matrix(3).ZERO);
}
test "matrix identity" {
expectMatrixEqual(3, [3][3]f32{ .{ 1, 0, 0 }, .{ 0, 1 , 0 }, .{ 0, 0, 1 } }, Matrix(3).IDENTITY);
}
test "matrix transpose" {
const actual = Matrix(3).init(.{ .{ 1, 2, 3 }, .{ 4, 5, 6 }, .{ 7, 8, 9 } });
const expected = [3][3]f32{ .{ 1, 4, 7 }, .{ 2, 5, 8 }, .{ 3, 6, 9 } };
expectMatrixEqual(3, expected, actual.transpose());
}
test "matrix multiplication" {
const A = Matrix(2).init(.{ .{ 1, 2 }, .{ 3, 4 } });
const B = Matrix(2).init(.{ .{ 6, 7 }, .{ 8, 9 } });
const expected = [2][2]f32{ .{ 27, 40 }, .{ 35, 52 } };
expectMatrixEqual(2, expected, A.mul(B));
}
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